Kenneth S. answered 10/13/17
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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018
suppose that you have a decimal fraction--0.32 for example
Multiply by two; you get 0.64; capture the digit (0 or 1) left of the decimal point, as the first bit after the binary point.
Repeat this step, multiplying by 2, stripping off the new 0 or 1 to make successive binary bits of the binary version. At each step,you will be doubling, and developing a zero or 1 bit. (If you developed a 1 bit units position by multiplying, it gets removed before the next doubling stage)...
2(.32) =0.64 gives .0 as first bit of the binary fraction
2).64)=1.28 gives next bit 1, so far we have .01
2(0.28)=0.56 gives next bit 0, so far we have .010
2(.56) gives next bit 1, so far we have .0101
2(.12) gives next bit 0, so far we have .01010
2(.24) gives next bit 0, so far we have .010100
2(48) gives next bit 0, so far we have .0101000
2(.96) gives next bit 1, so far we have .01010001 ... etc. etc.